Algebra 2 Hewitt

Standards for first semester

In this topic, students will:

• Recognize that sequences are functions with integer domains
• Recognize arithmetic sequences
• Connect arithmetic sequences with linear functions
• Identify common differences and find specified terms for arithmetic sequences
• Recognize geometric sequences
• Connect geometric sequences to exponential functions
• Identify common ratios and find specified terms for geometric sequences
• Write recursive and explicit definitions for the nth term in an arithmetic or geometric sequence
• Find sums for finite arithmetic and geometric series
• Use arithmetic and geometric sequences and series to model real-world situations
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• Recognize that the inverse of a relation is the set of ordered pairs obtained by interchanging the coordinates in each ordered pair
• Understand the graphical, tabular, and algebraic relationship between a linear function and its inverse
• Understand the relationship between exponential and logarithmic functions
• Understand the relationship between quadratic and square root functions
• Represent the inverse of a function using function notation
• Identify one-to-one functions
• Restrict the domain of a quadratic function in order for its inverse to be a function
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• Apply transformations to graphs of parent functions
• Recall key features of the linear, exponential, quadratic, and absolute value functions
• Describe a relationship based on its graph
• Recognize the general form of a quadratic equation and explain how the values of a, h, and k affect the shape of the parabola
• Describe and use the transformation from one function to another in terms of vertical shifts, vertical shrinks/stretches, and horizontal shifts
• Recognize that a piecewise function is made up of pieces of more than one function
• Generalize the transformations of all functions based on the values of a, h, and k
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• Recognize the general form of a polynomial function
• Identify the degree of a polynomial
• Perform mathematical operations on polynomial expressions
• Build polynomial functions from linear and quadratic functions
• Describe the increasing and decreasing behavior of quadratic and cubic functions
• Identify absolute and relative maximum and minimum values of quadratic and cubic functions
• Describe the domain and range of cubic functions
• Identify odd and even functions from graphs using symmetry
• Calculate average rates of change for quadratic and cubic functions
• Describe the concavity of the graph of a polynomial function
• Use interval notation to describe a set of values
• Understand the relationship between the degree of a polynomial and the number of real zeros it has
• Understand the relationship between the degree of a polynomial function and the number of local extreme values of the function
• Describe the end behavior of polynomials of odd and even degree
• Use polynomial functions to model real-world situations
• Describe the concavity of the graph of a polynomial function
• Use interval notation to describe a set of values
• Understand the relationship between the degree of a polynomial and the number of real zeros it has
• Understand the relationship between the degree of a polynomial function and the number of local extreme values of the function
• Describe the end behavior of polynomials of odd and even degree
• Use polynomial functions to model real-world situations
• Analyze situations modeled by polynomial equations
• Define and use imaginary and complex numbers in the solution of quadratic equations
• Use the discriminant of a quadratic equation to determine the number and type of roots of the equation
• Use polynomial long division and synthetic division to solve problems
• Factor the sum and difference of two cubes
• Factor polynomial expressions by grouping
• Solve polynomial equations with real coefficients by applying a variety of techniques in mathematical and real-world problems
• Understand the implications of the Fundamental Theorem of Algebra and the Remainder Theorem
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• Perform operations on rational expressions
• Build rational functions from rational expressions
• Simplify rational expressions by factoring
• Interpret models of rational functions
• Demonstrate transformations of functions on rational functions using parameter changes
• Find vertical asymptotes and removable discontinuities of rational functions
• Analyze the limiting or end behavior of functions and see how this behavior leads to horizontal asymptotes
• Find the domain and range of rational functions and restrict these for problem situations
• Move between the quotient form and the transformation form of a rational function
• Write rational equations to model problem situations
• Solve rational equations using graphs, tables, and analytic strategies
• Interpret solutions to rational equations in context using appropriate mathematical vocabulary
• Identify extraneous solutions